There is generally known a NOx catalyst for purifying nitrogen oxides (NOx) contained in an exhaust gas, as an exhaust purifying device arranged in an exhaust system for an internal combustion engine such as a diesel engine. Various types of NOx catalysts are known as the NOx catalyst, but among them, there is well known in public a selective catalytic reduction type NOx catalyst for sequentially reducing and removing NOx by addition of a reducing agent. Urea water or ammonia is known as the reducing agent. Urea water in which water and urea are mixed in a given ratio is usually injected and supplied in an exhaust gas upstream of the catalyst, and urea contained in the urea solution is hydrolyzed by heat of the exhaust gas or the like to generate ammonia. In addition, by a reduction function of the ammonia which removes oxygen from NOx on the NOx catalyst, which will be back to nitrogen, NOx in the exhaust gas is purified.
Patent Document 1 discloses the technology of adjusting an amount of urea water or ammonia to be added to a selective catalytic reduction type NOx catalyst for maintaining a high, stable NOx purifying rate. Specially in Patent Document 1, NOx sensors are provided respectively at the upstream side and at the downstream side of the selective catalytic reduction type NOx catalyst, an actual NOx purifying rate is calculated based upon output of these NOx sensors, and an addition amount of the reducing agent is adjusted based upon comparison between the actual purifying rate and a target purifying rate.    Patent Document 1: Japanese Patent Laid-Open No. 2003-293743